Assessing The Spatial Propagation Of West Nile Virus

In this work we study a spatial model for the West Nile Virus (WNV) propagation across the USA from the east to the west. WNV is an arthropod-borne flavivirus that appeared at first time in New York city in the summer of 1999 and then spread prolifically within birds. Mammals, as human and horse, do not develop sufficiently high bloodstream titers to play a significant role in transmission, which is the reason to consider the mosquito-bird cycle. The proposed model aims to study this propagation in a system of partial differential reaction-diffusion equations considering the mosquito and the avian populations. The diffusion is allowed to both populations, being greater in avian than in the mosquito. When a threshold value R0, depending on the model's parameters, is greater than one, the disease remains endemic and could propagate to regions previously free of disease. The travelling wave solutions of the model are studied to determine the speed of the disease propagation. This wave speed is obtained as a function of the model's parameters, for instance, vertical transmission rate and avian diffusion coefficient. © 2008 World Scientific Publishing Company.31-2227239Campbell, L.G., Martin, A.A., Lanciotti, R.S., Gubler, D.J., West Nile Virus (2002) The Lancet Infect Dis, 2, pp. 519-529Kenkre, V.M., Parmenter, R.R., Peixoto, I.D., Sadasiv, L., A Theoretical Framework for the Analysis of the West Nile Virus Epidemic (2005) Computer and mathematics with applications, 42, pp. 313-324Wonham, M.J., De-camino-Beck, T., Lewis, M.A., An epidemiological model for West Nile virus: Invasion analysis and control applications (2004) Proc. R. Soc. Lond. B, 271, pp. 501-507Cruz-Pacheco, G., Esteva, L., Montaño-Hirose, J.A., Vargas, C., Modelling the dynamics of the West Nile Virus (2005) Bulletin of Mathematical Biology, 67, pp. 1157-1172Bowman, C., Gumel, A.B., Van den Driessche, P., Wu, J., Zhu, H., A mathematical model for assessing control strategies against West Nile virus (2005) Bulletin of Mathematical Biology, 67, pp. 1107-1133Lewis, M., Renclawowicz, J., Van den Driessche, P., Travelling Waves and Spread rate for a West Nile Virus Model (2006) Bulletin of Mathematical Biology, 68, pp. 3-23Okubo, A., Diffusion-type models for avian range expansion (1998) Acta XIX Congressus Internationalis Ornithologici, pp. 1038-1049. , Henri Quellet, I, Ed, National Museum of Natural Sciences, University of Ottawa PressDeBiasi, R.L., Tyler, K., West Nile Virus Meningoencephalitis (2006) Nature Clinical Pratice Neurology, 2, pp. 264-275Harrington, L.C., Scott, T.W., Lerdthusnee, K., Coleman, R.C., Costero, A., Clarck, G.G., Jones, J.J., Edman, J.D., Dispersal of the Dengue Vector Aedes aegypti Within and Between Rural Communities (2005) Am. J. Trop. Med. Hyg, 72 (2), pp. 209-220Murray, J.D., Stanley, F.R.S., Brown, D.L., On the spatial spread of rabies among foxes (1986) Proc. R. Soc. Lond, B229, pp. 111-150Sandstede, B., Stability of traveling waves (2002) Handbook of Dynamical System II, pp. 983-1059. , B. Fiedler Ed, Elsevier, AmsterdamVolpert, A.I., Volpert, V.A., (1994) Traveling Waves Solutions of Parabolic System, , American Mathematical Society, Providence, RIMurray, J.D., (2002) Mathematical Biology, , Springer, Berli